Journal of Hydrology - msu.ru · detailed deterministic information (this information may include, for example, improved description of the main hydrological pro-cesses, accounting

Journal of Hydrology 388 (2010) 85–99

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Journal of Hydrology

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Extreme snowmelt floods: Frequency assessment and analysis of genesison the basis of the dynamic-stochastic approach

Alexander Gelfan *

Water Problems Institute of Russian Academy of Sciences, 119333, 3 Gubkin Str., Moscow, Russia

a r t i c l e i n f o s u m m a r y

Article history:Received 1 May 2009Received in revised form 9 March 2010Accepted 21 April 2010

This manuscript was handled byK. Georagakakos, Editor-in-Chief, with theassistance of Günter Blöschl, AssociateEditor

Keywords:Extreme floodSnowmeltDynamic-stochastic approach

0022-1694/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.jhydrol.2010.04.031

* Tel.: +7 499 1355 403; fax: +7 499 1355 415.E-mail address: [email protected]

A dynamic-stochastic approach, which combines a deterministic model of snowmelt runoff formationwith a stochastic weather generator, has been proposed. The model describes snow accumulation andmelt, vertical heat and moisture transfer in a soil, detention of melt water by the depressions at the catch-ment surface, overland and channel flow. The weather generator includes stochastic models that producedaily values of precipitation, air temperature, and air humidity during a whole year. Daily weather vari-ables have been simulated by Monte Carlo procedure and transposed to snowmelt flood hydrographs onthe basis of continuous simulation by the model of runoff generation. A specific censoring procedure hasbeen developed to select among the generated weather scenarios the ones that can lead to generation ofthe extremely high floods. The developed procedure makes simulations more efficient and computation-ally fast. The proposed approach has been used to generate extreme snowmelt floods exceeding the max-imum observed flood in the Seim River basin of central European Russia (catchment area, 7460 km2), toestimate their frequencies and, importantly, to assess characteristic conditions of the genesis of suchextreme floods.

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1. Introduction

Snowmelt flood generation is among the classic problems of thewatershed hydrology. A large number of hydrometeorologicalobservations and measurements has been accumulated for decadesand allowed hydrologists to develop a general understanding ofthe main processes that control generation of snowmelt floods un-der different physiographic conditions. However, due to the com-plexity and extreme spatial–temporal variability of theseprocesses, it is not possible to investigate flood generation and cre-ate methods of flood prediction based only on available observa-tions. Parallel with accumulating experimental data, theprospects are in developing models of snowmelt runoff generationwhich reflect the existing general understanding of the mainhydrological processes and use, in full measure, the availableobservations.

Typically, capabilities for improvement of the models are asso-ciated by their developers with accounting, as far as possible, moredetailed deterministic information (this information may include,for example, improved description of the main hydrological pro-cesses, accounting for peculiarities of the specific basin, assimilat-ing new experimental data, etc.). As a result, a substantial advancehas been made in the development of the watershed models,

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including snowmelt runoff models of different sophistication, e.g.IHDM (Morris, 1983), SHE (Abbott et al., 1986; Bathurst andCooley, 1996), Hydrological Cycle Lab. Model (Kuchment et al.,1986), MIKE-SHE (Refsgaard and Storm, 1995), VIC-3L (Woodet al., 1997), ECOMAG (Motovilov et al., 1999), WASIM-ETH(Verbunt et al., 2003), HL-RMS (Koren et al., 2004), CRHM(Pomeroy et al., 2007) and many others. But whatever detaileddeterministic model supplied with all needed data would be devel-oped, the uncertainty still remains over some spatial–temporalscales indescribable by this model. To account for different sourcesof such an uncertainty, the appropriate stochastic informationshould be included in the model. Development of such a modelwhich is based on the deterministic description of the hydrologicalprocesses and takes into account available stochastic information(on input variables, basin characteristics, model parameters, etc.)is the subject of the dynamic-stochastic approach to hydrologicalmodeling.

Development of the hydrological model with random forcing isthe dynamic-stochastic approach which allows one to account forthe stochastic nature of the meteorological processes driving run-off generation. The resulting model integrates two components:deterministic model of runoff generation and stochastic modelsof the meteorological variables providing the inputs into determin-istic model. Such integration opens up fresh opportunities fordeveloping new approaches to flood frequency assessment andunderstanding processes of extreme flood generation.

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86 A. Gelfan / Journal of Hydrology 388 (2010) 85–99

Eagleson (1972) was probably the first who proposed the dy-namic-stochastic approach based on the derived distribution tech-nique to obtain relationship between frequencies of rainfall floodon the one hand and probabilistic properties of rainfall as well asphysical characteristics of river basin on the other hand. In the con-text of the rainfall flood frequency estimation, the derived distribu-tion technique has been used and extended by Chan and Bras(1979), Hebson and Wood (1982), Diaz-Granados et al. (1984),Blöschl and Sivapalan (1997), Goel et al. (2000) and others. In orderto be in the framework of the analytical approach, the authors ofthese works employed simplification in both the hydrologic mod-els and the stochastic models of meteorological inputs.

An alternative numerical technique for deriving flood frequencyis in using Monte Carlo simulations of meteorological inputs. Sucha technique allows one to avoid undue simplifications and to com-bine a rather sophisticated model of runoff generation with a sto-chastic weather generator. A rainfall–runoff model was firstcombined with the Monte Carlo continuous simulation of precipi-tation series by Kuchment et al. (1983). Recently, numericaldynamic-stochastic approach was applied by Sivapalan et al.(1990), Franchini et al. (1996), Blazkova and Beven (1997),Hashemi et al. (2000), Sivapalan et al. (2005), Haberlandt et al.(2008) which used different rainfall–runoff models (TOPMODEL,ARNO, HEC-HMS and others) for derivation of flood frequency.

The body of work listed above was carried out for the estima-tion of the rainfall flood frequency. It has been well-established(for example, Loukas et al., 2000; Merz and Blöschl, 2003) that sig-nificant difference exists between frequency statistics of rainfallfloods and floods of snowmelt origin resulted from the differencesin causative flood mechanisms. In spite of the importance of theproblem of snowmelt flood in many countries (e.g. in Russia morethan 65% of the disastrous floods registered from 1985 to 2005were because of melt of snow), only few dynamic-stochastic stud-ies dealt with this problem. Velikanov (1949) made the first at-tempt to calculate frequency of the snowmelt flood peakdischarge as a function of maximum snow water equivalent andsnowmelt duration. Carlson and Fox (1976) applied the model ofEagleson (1972) for deriving frequency curve of snowmelt floodpeak discharge. Kuchment and Gelfan (1991, 2002), Blazkova andBeven (2004) combined models of snowmelt flood generation withstochastic weather generator and estimated frequency of snow-melt floods on the basis of continuous simulation.

Possible applications of the dynamic-stochastic approach is notrestricted by frames of the flood frequency assessment and expandto the problem of understanding the processes of extreme floodgeneration (the examples of such applications presented by Siva-palan et al. (1990, 2005), Franchini et al. (2000), Fiorentino et al.(2007) among others). The applicability of a dynamic-stochasticapproach to this problem depends, first of all, on the physical valid-ity of the hydrological model associated with its ability to repro-duce behaviour of the hydrological system in unobservedsituations. From this viewpoint, use of a physically based modelfounded on fundamental physical principles and utilizing a largeamount of a priori information on the processes constituting thehydrological systems, looks attractive. However practical applica-tion of such a model combined with the Monte Carlo simulationsof weather inputs may become computationally unreasonable. In-deed, in order to obtain a stable estimation of extreme floods of aspecified return period, one should simulate runoff series whichare more than one order of magnitude longer than the return per-iod (see, for example, Franchini et al., 1996; Blazkova and Beven,1997; Loukas, 2002). Thus, the problem in applying sophisticatedmodels is to reduce, as much as possible, time of computationsneeded to obtain stable estimations of extreme floods. An approachto such a reduction was suggested in the paper of Fiorentino et al.(2007) for a model of rainfall flood generation. According to their

approach, the simulation process is activated by means of dailygenerated rainfall inputs, which are required to run simplifiedhydrological model with the main purpose of providing the initialconditions for event simulations. This model runs as long as a dailyrainfall rate greater than the pre-determined threshold does notoccur. Whenever this threshold is exceeded, the simulationswitches to full hydrological model in order to reproduce the floodevent. Thus, the essence of the approach suggested by Fiorentinoet al. (2007) is in preliminary selection of simulated rainfall thatcould potentially result in extreme rainfall flood and driving thehydrological model by the selected inputs only.

The main objectives of the paper are to present: (1) physicallybased model of snowmelt flood generation coupled with stochasticweather generator extending the approach developed by Kuchmentand Gelfan (2002); (2) a new procedure for preliminary selection ofthe meteorological conditions controlling extreme snowmelt floodsto make their simulations more efficient and computationally fast;and (3) to demonstrate applicability of the presented dynamic-stochastic approach for assessment of extreme flood frequencyand investigation of the processes controlling formation of extremesnowmelt floods.

2. Study basin

Seim River is a part of the Dnieper river basin and located in thesteppe-forest physiographic zone of the European Russia. Thecatchment area is 7460 km2 at the basin outlet in Kursk(51�380N, 36�110E). The relief of the basin is a rugged plain withmany river valleys, ravines, and gullies. The soils are mainly cher-nozem and podzol. The ground water level fluctuates at 15–30 mbelow the land surface. Most part of the basin (about 70%) isploughed; forests occupy about 10%; pastures take up about 19%;urbanized lands occupy less than 1%. Annual precipitation is about650 mm, over 40% of which falls as snow; mean snow water equiv-alent before melt is 89 mm. Mean date of the beginning of snow-melt is March 24. During the snowmelt period, which is 3 weeksin average, from 30% to 80% of annual runoff is generated (61% inaverage). Mean snowmelt runoff depth is 69 mm; mean peak dis-charge of snowmelt flood is 592 m3 s�1 (note, that the latter valueis much greater than the highest observed peak discharge of rain-fall flood – 109 m3 s�1). The highest peak discharge of snowmeltflood was 2230 m3 s�1 on 23 April 1929.

3. Dynamic-stochastic approach to modeling snowmelt floods

The developed model consists of two components: physicallybased model of snowmelt runoff generation and stochastic modelsof weather variables (weather generator). The physically basedmodel is improved in comparison with the model presented byKuchment and Gelfan (2002) and described below in more detail.

3.1. Model of snowmelt runoff generation: structure and parameterassessment

3.1.1. Description of the modelThe model of snowmelt runoff generation describes snow accu-

mulation and melt, water and heat transfer in a soil during itsfreezing and thawing, infiltration into frozen and unfrozen soil,detention of melt water by basin storage, overland and channelflow. Finite-element discretisation of the Seim catchment area isused (Fig. 1). The channel river system represented by the SeimRiver and its main tributaries is divided into 69 reaches (finite ele-ments) taking into account the topography and the river networkstructure; the basin area is separated onto strips, adjacent to thechannel finite elements and along which one-dimensional flow to

(a)

(b)

Fig. 1. Finite element schematization (a) of the Seim catchment and distribution of soils (b) over the catchment area. 1 – catchment boundaries; 2 – channel network; 3 –runoff gauges; 4 – agrometerological stations; 5–8 – soil types: 5 – sierozem, 6 – podzol, 7 – typical chernozem, 8 – meadow soil.

A. Gelfan / Journal of Hydrology 388 (2010) 85–99 87

river channels is assumed. The strips also are divided into finiteelements with different characteristics of topography and soils.The total number of the elements over the whole catchment areais 367.

To calculate the characteristics of snow within each element,the system of vertically averaged equations of snow processeshas been applied (Gelfan et al., 2004). The system is written asfollows:

dHs

dt¼ qw Xsq�1

0 � ðM þ EsÞðqiIsÞ�1h i

� V ð1Þ

ddtðqiIsHsÞ ¼ qwðXs �M � EsÞ þ Fi ð2Þ

ddtðqwhsHsÞ ¼ qwðXl þM � El � RsÞ � Fi ð3Þ

where H is the snow depth; I and hs are the volumetric content of iceand liquid water, respectively; Xs and Xl are the snowfall rate and

Table 2Stochastic weather generator parameters estimated by the long-term meteorologicalobservations in the Seim River basin (standard deviations of the estimations areshown in brackets).

Parameter Period of simulation

May–October November–April

Model of daily precipitationProbability of dry day after dry day 0.70 (0.06) 0.63 (0.06)Probability of wet day after wet day 0.56 (0.07) 0.67 (0.06)Mean of daily precipitation amount, mm 4.74 (0.90) 2.59 (0.62Coefficient of variation of daily

precipitation amount1.40 (0.26) 1.36 (0.18)

Model of daily air temperatureNovember–April

Mean seasonal temperature, �C �3.27 (0.18)Standard deviation of mean seasonal temperature, �C 1.68 (0.12)

Model of daily air humidity deficitMay–October

Mean air humidity deficit for the dry spell, mb 6.52 (0.53)Standard deviation of mean air humidity deficit, mb 1.59 (0.19)Coefficient of correlation between the mean air

humidity deficit and duration of the dry spell0.72 (0.11)


the rainfall rate, respectively (partitioning of the total precipitation,X, into solid and liquid phase is a function of the air temperature, Ta:

Xs = aXX; Xl = (1 � aX)X, where aX ¼0; Ta > 0 �C1; Ta 6 0 �C

�); M is the melt

rate determined as M ¼ ksqsTa; Ta > 0 �C0; Ta 6 0 �C

�; qs is the density of

snowpack equalled qs = qiIs + qwhs; qw, qi, and q0 are the densityof water, ice, and fresh-fallen snow, respectively; El and Es arethe evaporation and sublimation rates, respectively, calculatedas El ¼ kEda

qwhsqs

; Es ¼ kEdaqi Isqs

; da is the air humidity deficit; Fi is

the rate of refreezing of melt water in snow, Fi ¼ksqs

ffiffiffiffiffiffiffiffijTaj

p; Ta < 0 �C ^ hs > 0

0; Ta P 0 �C _ hs ¼ 0

�, Rs is the meltwater outflow from

snowpack calculated taking into account the maximum liquidwater-retention capacity hmax = 0.11(1 � qs/qw), V is the snowpack

compression rate determined as (in cm h�1) V ¼ �0:01qsexpð�0:08Taþ21qsÞ

H2s

2

(here qs is in g cm�3); ks and kE are the empirical coefficients whichare related to the assumed linear dependences of a degree-day fac-tor on snow density and snow evaporation rate on air humidity def-icit, respectively.

Water and heat transfer in a soil during the processes of soilfreezing, thawing and infiltration of water are described by thefollowing equations (Gelfan, 2006):

@W@t¼ @

@zD@h@zþ DI

@I@z� K

� �ð4Þ

cT@T@t� qwL

@W@t¼ @

@zk@T@z

� �þ qwcw D

@h@zþ DI

@I@z� K

� �@T@z

ð5Þ

where W, h and I are the total water content, liquid water content

and ice content of soil, respectively W ¼ hþ qiqw

I� �

; K = K(h, I) is

the hydraulic conductivity of soil; T is the temperature of soil;k ¼ kðh; IÞ is the thermal conductivity; D ¼ K @w

@h

� I; DI ¼ K @w

@I

� h;

w ¼ wðh; IÞ is the matrix potential of soil; cT ¼ ceff þ qwL @h@T; ceff is

the effective heat capacity of soil equals ceff = qgcg(1 � P) + qwcwh +qiciI; q and c are the soil density and the specific heat capacity,respectively (indexes w, i and g refer to water, ice and soil matrix,respectively); P is the soil porosity; L is the latent heat of ice fusion.

The matrix potential, w = w(h, I), and the hydraulic conductivity,K = K(h, I), of soil are determined from the following formulas(Gelfan, 2006):

Table 1Parameters of the model of runoff generation in the Seim River basin.

Mathematical symbol Physical meaning

Parameters distributed over the catchment area in dependence on soil typeh0 Saturated water contenthr Residual water contenta, cm�1 Parameters of the formulae of Van Genuchten (1980)nCg, J kg�1 C�1 Specific heat capacity of ground matrixk, J m�1 s�1 �C�1 Thermal conductivityK0, m s�1 Saturated hydraulic conductivity

Lumped parametersks, m4 �C�1 kg�1 s�1 Empirical coefficient of formnr, s m�1/3 Manning’s coefficient of rouns, s m�1/3 Manning’s coefficient of rouKE, m hPa�1 s�1 Empirical coefficient of formKE, m hPa�1 s�1 Empirical coefficient of formDET0, m Mean value of the free storq0, kg m�3 Density of fresh-fallen snow

wðh; IÞ ¼�ðS�1=m�1Þ1=n

a� h0� hr

h0� I� hrþ hr

h1� h0� hr

h0� I� hr

� � �ð1þ8IÞ2

ð6Þ

Kðh; IÞ ¼ K0S0:5 1�ð1� S1=mÞm

1þ8I

" #2

ð7Þ

where S ¼ h�hrh0�I�hr

is the relative saturation of soil; h0 and hr are thesaturated and residual water contents, respectively; K0 is the satu-rated hydraulic conductivity; a and n are the parameters (vanGenuchten, 1980) which are related to the inverse of the air entrypressure and the pore-size distribution, respectively; m ¼ 1� 1

n.Infiltration of melt water into soil is calculated from Eq. (4). For

unfrozen soil (I(z, t) = 0), Eq. (4) reduces to the diffusion form of theRichard’s equation, and formulas (6), (7) reduce to the known for-mulas w = w(h) and K = K(h) of van Genuchten (1980).

Eqs. (4) and (5) are numerically integrated by an implicit, four-point finite difference scheme; the corresponding difference equa-tions are solved by the double-sweep method. The temporal andspatial steps of the finite difference scheme are 10,800 s and

Numerical value

Sierozem Podzol Typical chernozem Meadow soil

0.49 0.56 0.52 0.530.09 0.07 0.05 0.050.06 0.01 0.02 0.021.48 1.23 1.27 1.33Depends on soil temperature and moisture content (Gelfan, 2006)Depends on soil temperature and moisture content (Gelfan, 2006)1.07 � 10�5 0.76 � 10�5 2.16 � 10�5 1.88 � 10�5

ula of melt rate 2.2 � 10�10

ghness for the river channels 0.07ghness for the slope surface 0.13ula of soil evaporation rate 8.0 � 10�8

ula of snow evaporation rate 2.9 � 10�8

age capacity 0.01120


0.1 m, respectively. The adopted iteration algorithm is described in(Gelfan, 2006).

Cumulative detention, DETR, of melt water by surface depres-sions is calculated by the formula assuming exponential distribu-tion of the storage capacity (Kuchment and Gelfan, 2002):

DETR ¼ DET0 1� exp � rR

DET0

� � �ð8Þ

where DET0 is the mean value of the free storage capacity before thebeginning of melt; RR is the cumulative snowmelt outflow fromsnowpack.

01 March-30 April 1981

050

100150200250300350

24.02 15.03 04.04 24.04 14.05

24.02 15.03 04.04 24.04 14.05

24.02 15.03 04.04 24.04 14.05

24.02 15.03 04.04 24.04 14.05

24.02 15.03 04.04 24.04 14.05

Date

Q, m3 s-1


0

50

100

150

200


0

100

200

300

400

500


0

100

200

300

400

500

600


050

100150200250300350400

Fig. 2. Comparison of observed (bold line) and simulated (thin line) hydrographs of snvalidation period).

The rate of evaporation, E, from an unfrozen, snow-free soil iscalculated as:

E ¼ KEdaS1 ð9Þ

where S1 is the relative saturation of the upper soil layer; KE is theempirical coefficient.

Overland flow is the main mechanism of water inflow to riverchannels; subsurface contribution is negligible, so it is not consid-ered by the model. To simulate overland and channel flow, the one-dimensional kinematic wave equations numerically integrated bythe finite-element method are applied (Kuchment et al., 1986).

24.02 15.03 04.04 24.04 14.05

24.02 15.03 04.04 24.04 14.05

24.02 15.03 04.04 24.04 14.05

24.02 15.03 04.04 24.04 14.05

24.02 15.03 04.04 24.04 14.05


0

500

1000

1500

2000


0

200

400

600

800

1000

1200


0

50

100

150

200


0

50

100

150

200

250

300


050

100150200250300350400

owmelt floods in the Seim river (left column – calibration period; right column –


The equations contain two parameters, namely, Manning rough-ness coefficients for overland and channel flow (ns and nr,respectively).

Runoff excess is calculated by Eqs. (1)–(9) for each finite ele-ment taking into account the sub-element variability of snowwater equivalent before spring melt and saturated hydraulic con-ductivity of soil. Sub-element variability is described by two-para-metric gamma-distribution function of the respective spatialvariable within an element. Parameters of gamma distributionare assigned by the following way. Mean value of pre-melt snowwater equivalent within an element before spring melt is calcu-lated by the snow model (1)–(3). Mean value of saturated hydrau-lic conductivity for each type of soil within an element is identifiedas shown in the next sub-section. Variances of snow water equiv-alent and saturated hydraulic conductivity within an element arecalculated with the help of their dependences on the correspond-ing mean values (Kuchment et al., 1986, 1996). Each of two ob-tained gamma distributions is represented as a number of classes(i.e. each distribution is discretized) and the model equations areapplied to each class. The total number of classes equals to productof classes representing the distributions, since snow water equiva-lent and hydraulic conductivity of soil are statistically indepen-

1960

0

500

1000

1500Q, m3s-1

1963

0

500

1000

1500

1970

0500

100015002000

1971

0300600900

1200

1979

0

300

600

900

1200

15.03 25.03 04.04

15.03 25.03 04.04

15.03 25.03 04.04

15.03 25.03 04.04

15.03 25.03 04.04

Fig. 3. Comparison of observed (bold line) and simulated (thin line) hydrogra

dent. The finite-element response is then the weighted sum ofthe responses of the classes.

3.1.2. Parameter identificationThe presented model contains 14 parameters. Seven parameters

(the coefficients a and n as well as the saturated, h0, and residual,hr, water contents of formulas (6), (7), the heat capacity, cT, thethermal conductivity, k, and the saturated hydraulic conductivity,K0) are assumed to vary over the catchment area depending on soiltype. For each type of soil within a finite element, the listed param-eters (except K0) are assessed from the available soil survey mea-surements at the Seim River basin. The values of h0 and hr areassumed to be equal to the measured soil porosity and maximumhydroscopicity, respectively. The values of a and n are calculatedfrom the measured soil characteristics, such as bulk density, fieldcapacity, and wilting point. The values of cT, and k are calculatedby the dependences on soil temperature, ice and liquid water con-tent as well as the same measured soil characteristics. The corre-sponding relationships for calculation of a, n, cT, and k arepresented in Gelfan (2006). Preliminary values of K0 for typicalsoils of the Seim River basin are adopted from (Nazarov, 1970).

Date

14.04 24.04 04.05

14.04 24.04 04.05

14.04 24.04 04.05

14.04 24.04 04.05

14.04 24.04 04.05

phs of the highest snowmelt floods in the Seim river (validation results).


Seven parameters are assumed to be constant over the catch-ment area: three parameters of snow model (ks, q0, and kE), param-eters DET0 and KE of Eqs. (8) and (9) as well as the Manningroughness coefficients ns and nr. The values of snow model param-eters as well as evaporation parameter kE are adjusted through cal-ibration against snow and evaporation measurements at a smallproxy-basin (Yasenok Creek; catchment area is 21 km2) located80 km to the east from the Seim River basin. In detail, the proce-dure of the parameter assessment using the Yasenok Creek mea-surements is presented in Kuchment and Gelfan (2009).

The values of the parameters (both assessed from the soil mea-surements in the Seim River basin and calibrated using the mea-surements in the proxy-basin) contain a large degree ofuncertainty. The uncertainty is an inherent property of a hydrolog-ical model arising from inadequacy of the model to the natural pro-cesses involved, impossibility to specify the initial and boundaryconditions with required accuracy, discrepancy of point-scaleequations to the scale of the natural processes, measurement er-rors, etc. For this reason four parameters of the model (DET0, nr

as well as preliminary assessed K0 and ks) are adjusted through cal-ibration against measured discharges at the Seim River basin outletfor 10 years (1979–1988). The calibrated parameters are assessedas follows: DET0 = 0.01 m; nr = 0.07 s m�1/3; ks = 2.2 � 10�10

m4 �C�1 kg�1 s�1, K0 = 0.76 � 10�5–2.16 � 10�5 m s�1 depending

Table 3Observed and simulated flood volumes (Y, mm) and peak discharges (Qmax, m3 s�1) for th

Date of the peak Observed Calculated

Y0 Q0 Yc Qc

14.04.1969 68 548 46 36507.04.1970 167 1790 182 189026.03.1971 70 1080 77 105021.03.1972 23 116 25 17530.03.1973 31 284 34 21324.03.1974 37 346 34 26112.03.1975 18 42 19 6709.04.1976 21 139 21 12830.03.1977 37 195 22 7528.03.1978 60 415 42 20603.04.1979 94 1030 88 90709.04.1980 51 433 57 40429.03.1981 55 333 41 23902.04.1982 54 340 50 35628.03.1983 45 273 53 41701.04.1984 33 154 35 15808.04.1985 43 343 60 62726.03.1986 61 394 52 32916.04.1987 51 478 50 44130.03.1988 66 416 69 592

Mean 54 457 53 445

Table 4Observed and simulated flood volumes (Y, mm) and peak discharges (Qmax, m3 s�1) of the

Date of the peak Observed Calculated

Y0 Q0 Yc Qc

23.04.1929 130 2230 148 215611.04.1932 137 2220 122 192007.04.1970 167 1790 182 189029.03.1951 112 1410 121 149102.04.1960 103 1360 101 111217.04.1963 102 1240 101 120026.03.1971 70 1080 77 105003.04.1945 87 1060 104 113031.03.1947 112 1040 98 90303.04.1979 94 1030 88 907

Mean 111 1446 114 1376

on the soil type. The complete list of the model parameters is pre-sented in Table 1.

3.2. Stochastic weather generator

The weather generator (WG) is a set of stochastic models thatuse existing weather records to produce long series of syntheticdaily weather variables, which statistical properties are expectedto be similar to those of the actual data. The used WG was pre-sented in a recent paper (Kuchment and Gelfan, 2002). It includesstochastic models of daily precipitation, air temperature and theair humidity deficit. To represent the tendency of wet or dryweather spells to persist, the widely-used two-state, first-orderMarkov chain is applied. Daily precipitation amount is consideredas a gamma distributed random variable with different parametersfor the cold season and for the warm one. For the dry spell, theaverage air humidity deficit is considered as a lognormal variable;for the wet spell, the air humidity deficit was set equal to zero. Inorder to simulate the air daily temperature occurrences, so-calledmethod of fragments (Srikanthan and McMahon, 1985) is applied.

Time-series of daily precipitation, air temperature and humiditydeficit observed in the meteorological stations located at the Seimcatchment for 101 years (1891, 1892, 1896–1941, 1943–1995) areutilized for estimating the parameters of the developed stochastic

e period from 1 March to 30 April (the calibration period is shown by gray).

Errors

Yc � Y0 Qc � Q0 (Yc � Y0)/Y0 (Qc � Q0)/Q0

�22 �183 �0.33 �0.3315 100 0.09 0.06

7 �30 0.10 �0.032 59 0.10 0.513 �71 0.10 �0.25�3 �85 �0.07 �0.25

1 25 0.08 0.590 �11 0.01 �0.08

�15 �120 �0.41 �0.62�18 �209 �0.30 �0.50�6 �123 �0.06 �0.12

6 �29 0.11 �0.07�14 �94 �0.25 �0.28�4 16 �0.08 0.05

8 144 0.20 0.532 4 0.07 0.02

17 284 0.38 0.83�9 �65 �0.14 �0.16�1 �37 �0.01 �0.08

3 176 0.05 0.42

�1 �12 �0.02 �0.01

highest snowmelt floods in the Seim River.

Errors

Yc � Y0 Qc � Q0 (Yc � Y0)/Y0 (Qc � Q0)/Q0

18 �74 0.14 �0.03�15 �300 �0.11 �0.14

15 100 0.09 0.069 81 0.08 0.06�2 �248 �0.02 �0.18�1 �40 �0.01 �0.03

7 �30 0.10 �0.0317 70 0.20 0.07�14 �137 �0.13 �0.13�6 �123 �0.06 �0.12

3 �70 0.03 �0.05


models on mean areal basis. Parameters of the precipitation modelare estimated by the methods presented by Katz (1977). Parame-ters of the air temperature and humidity models are estimatedby the method of moments. The complete list of the weather gen-erator parameters is presented in Table 2.

3.3. Censoring Monte Carlo simulated meteorological inputs forestimating floods of low probabilities

Let us assume that it is necessary to estimate flood peak dis-charge QP of very low exceedance probability (say, Pr = 0.001) onthe basis of a hydrological model with using Monte Carlo simula-tions of meteorological inputs. The following technique is typicallyapplied in the previously cited studies. Multi-year (say,10,000 years) artificial meteorological series are generated as in-puts into the hydrological model and 10,000 corresponding annualpeak floods are simulated by the model. The exceedance probabil-

Autocorrelatio

-0.2

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

la

Cor

r(X

n,X

n+l)

Frequency histog

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

1 2 3 4 5

Fre

quen

cy

Cumulative probabilpre

0.00

0.20

0.40

0.60

0.80

1.00

0 20 40Precipi

Cum

ul. p

roba

bilit

y

Observa

Observation

Observatio

Fig. 4. Comparison between statistical properties of

ities are estimated for the calculated flood peak discharges and thedesired quantile Q0.001 is obtained. As long as 10,000 flood peakdischarges have been calculated, consequently the obtained valueof Q0.001 is close to the 10th term of the ranged discharge series.It means that only 10 from 10,000 simulated flood hydrographsare really needed to estimate the desired quantile Q0.001, i.e.99.9% of simulations have appeared redundant. In the case of usingsophisticated, time-consuming hydrological model (as presentedherein through Eqs. (1)–(9)) such an approach is computationallywasteful. It would be reasonable, before the hydrological simula-tions, to find thousands of the generated weather scenarios whichcertainly cannot result in extreme simulated floods. After which,the hydrological model can be run under the remaining weatherscenarios only. Hereafter, the weather scenario is determined asthe 1-year (from May 1 to April 30) time-series of daily generatedmeteorological data. The weather scenario is used as an input intothe hydrological model to simulate a single snowmelt flood hydro-

n of precipitation

5 6 7 8 9 10

g, day

rams of wet intervals

6 7 8 9 10Days

ities of annual maximum cipitation

60 80 100 120tation, mm/day

tions Model

s Model

ns Model

the observed and modeled precipitation series.


graph, i.e. each simulated hydrograph is in accordance with therespective weather scenario.

We developed the following procedure for selection of suchartificial weather scenarios which can result in simulated floodpeak discharges Qmax P Q*, where Q* is the pre-determinedthreshold:

1. N1 meteorological scenarios are simulated by the weather gen-erator. Time series of the melt water outflow from snowpackRi(t) (i = 1,2, . . . , N1) are simulated by the snow model (Eqs.(1)–(3)) for each of N1 scenarios. (Numerical solution of Eqs.(1)–(3) is fast, particularly, two order faster than solution ofEqs. (4) and (5)).

2. Maximum possible peak discharge QMAXi (i = 1,2, . . . , N1) foreach ith weather scenario is calculated.In order to calculate QMAXi, the time series of Ri(t) simulated atthe 1st step of the procedure are used as inputs into the modelof overland and channel flow. We do not take into account run-off losses, i.e. flood routing over the catchment slopes and inriver channels is the only hydrological process modeled in thisstep. The full model (1)–(9) accounts for the runoff losses (infil-tration, evaporation, etc.). So if the model (1)–(9) was applied tocalculate Qmax i under the same ith weather scenario, then Qmax i

would be less than QMAXi. Consequently, if the obtained maxi-mum possible peak discharge QMAXi is less than Q*, then thecorresponding Qmax i will be definitely less than Q*. In otherwords, we find, before applying the complete model, that ithweather scenario certainly can not result in desired flood.

(a)

0

500

1000

1500

2000

2500

3000

3500

0.001 0.01

Qm

ax, m

3 s-1

(b)

0

50

100

150

200

250

0.001 0.01

Exceeda

Y, m

m

Fig. 5. Exceedance probabilities of the simulated extreme floods (black points) and the ovalues. a – Flood peak discharge and b – flood volume.

Otherwise, if for some jth scenario QMAXj > Q*then the modelcan, potentially, calculate Qmax j > Q*under the same jth weatherscenario and this scenario should be used for further modeling.Finally, after this step N2 (N2 < N1) weather scenarios areselected which met the condition QMAXj > Q* (j = 1,2, . . . , N2).

3. N2 floods are simulated by the model (1)–(9) under the selectedweather scenarios. From the calculated sample of Qmax j, N3 val-ues (N3 < N2) are selected which met the condition Qmax n PQ*(n = 1,2, . . . , N3) and the corresponding exceedance probabil-ities are estimated as Pr Q rang

n P Q ��

¼ nN1

where Q rangn is the

ranged sample of Qmax n.

As a result, we obtain censored sample of the calculated floodpeak discharges Qmax because we know N3 censored values ofQmax n over threshold Q* and the number (N1–N3) of the remainingvalues however most of these values are unknown. (Note, that thisis type I censoring where the threshold is known and the numberof the censored data points varies.)

Similar censoring procedure was applied to estimate exceed-ance probabilities of flood volumes Y over some pre-determinedthreshold Y* (Y > Y*). The only difference is that the criterion usedto select appropriate weather scenarios, YMAXi, is defined:

YMAXi ¼ SWEmaxiþ RXi ð10Þ

where SWEmaxiis the maximum pre-melt snow water equivalent

calculated by the snow model (Eqs. (1)–(3)) for ith scenario; RXi

is total precipitation over the snowmelt period for ith scenario

0.1 1

0.1 1

nce probability

bserved floods (white points). Line is the gamma distribution fitted to the observed


(the duration of the ith snowmelt period is also calculated by thesnow model).

The value of YMAXi is the maximum possible flood volumewhich can, potentially, formed under the specific weather scenarioand in the absence of runoff losses. As with the case of Q*, the mod-el is not run for the ith weather scenario if YMAXi < Y*.

4. Results and discussion

4.1. Validation of the model of runoff generation

To validate the model of runoff generation, two tests were con-ducted against the measured discharges at the Seim River basinoutlet. During the first one, runoff hydrographs were simulatedfor the period of 1969–1978 and compared with the observed ones.

-9 -8 -7 -6 -

Mean winter te

0%

3%

5%

8%

10%

13%

15%

18%

21%

23%

26%

28%

31%

Num

ber o

f ext

rem

e flo

ods,

%

(a)

18/03 20/03 22/03 24/03 26/03 28Date of begin

0%

3%

5%

8%

10%

13%

15%

18%

21%

23%

Num

ber o

f ext

rem

e flo

ods

Climatic m(b)

Fig. 6. Frequencies of occurrence of the simulated extreme floods under the different

During the second validation test, we compared the simulated andthe observed characteristics (volumes and peak discharges) of 10highest floods registered at the Seim River. Simulated and observedhydrographs for both calibration and validation periods are shownin Figs. 2 and 3. Note that not all of the highest floods are shown inFig. 3 because for the floods of 1929, 1932, 1945, 1947, and 1951we do not have daily discharge data (volumes and peak dischargesare available only). Runoff volumes, Y, and peak discharges, Qmax,for all simulated floods are shown in Tables 3 and 4. As one cansee from these Tables, mean errors of calculations of Y and Qmax

are close to zero. Root mean square errors (RMSE) are 10 mm(for Y) and 119 m3 s�1 (for Qmax) for 20 floods of 1969–1988; RMSEfor 10 highest floods are 12 mm and 136 m3 s�1, respectively Theefficiency criteria, NSY and NSQ, of Nash and Sutcliffe (1970) wasalso adopted to summarize the goodness of fit of the simulated

5 -4 -3 -2 -1 0

mperature of air,ºС

Climatic mean = -3.4ºC

/03 30/03 01/04 03/04 05/04 07/04 09/04ning of spring melt

ean: 24 March

mean winter temperature (a) and date of the beginning of spring melt period (b).


and observed values of Y and Qmax, respectively. For 10 floods ofvalidation period (1969–1978), NSY = 0.93; NSQ = 0.94. For 10 high-est floods NSY = 0.81; NSQ = 0.90. It is seen from these results thatthe model satisfactory passes both validation tests.

However there are some rather large relative errors in calculat-ing both flood volume and peak discharge. As a role, the major er-rors are for the low floods, whereas the highest floods arecalculated with good accuracy. Taking into account sparseness ofthe available observational points (see Fig. 1) utilized for assigningthe input data and soil characteristics, one can assume that theseerrors are caused, to a large degree, by the uncertainty in descrip-tion of spatial heterogeneity of the flood generation processes. Thisheterogeneity is more visible and plays the more important rolewhen low floods are generated. In the forest-steppe watersheds,spatial variances of snow water equivalent, soil freezing depth, soilmoisture content increase with decreasing of the correspondingmean values (Vershinina et al., 1985). These spatial variances aresmoothed by the model that results in relatively large simulationerrors.

4.2. Validation of the weather generator

The stochastic models were comprehensively tested through itsability to reproduce the main features of meteorological processesat the Seim River basin. For testing, we compared only those char-acteristics of the observed and simulated time-series which areneither the parameters of the models nor a single-valued functionof the parameters. The following characteristics of the observedand simulated time-series of precipitation were compared: histo-grams of wet and dry spell durations, autocorrelation functionsof precipitation occurrence and daily precipitation series, varianceof precipitation sum for 30 and 365 successive days, distribution ofmaximum daily precipitation for 30 and 365 successive days. Forthe model of air temperature we tested how the model reproducesmean value and variance of air temperature for 30 successive daysand autocorrelation function of temperature time-series. Histo-grams of mean air humidity deficit for dry spell intervals of differ-ent duration were compared for testing the model of air humiditydeficit. Some results demonstrating comparison between statisti-

120 140 160 180 200 220Total of winte

0%

3%

5%

8%

10%

13%

15%

18%

21%

23%

Num

ber o

f ext

rem

e flo

ods,

%

Clim

Fig. 7. Frequencies of occurrence of the simulated extre

cal properties of the observed and simulated precipitation seriesare shown in Fig. 4.

4.3. Assessment of frequency of extreme floods

For flood peak discharges, we assigned the thresholdQ* = 2200 m3 s�1 that is close to the maximum observed dischargeat the Seim River. Ten thousand (N1 = 10,000) weather scenarioswere Monte Carlo generated and 10,000 values of QMAXi werecalculated. From 10,000 scenarios, 617 scenarios (N2 = 617) wereselected which met the condition QMAXj > 2200 m3 s�1, i.e. only6.17% of the generated weather scenarios could, potentially, resultin Qmax > 2200 m3 s�1. Then, 617 snowmelts floods were simu-lated by the model under the selected weather scenarios, andN3 = 78 from 617 simulated floods were selected which met thecondition Qmax > 2200 m3 s�1. The exceedance probabilities werecalculated for Qmax > 2200 m3 s�1 and are shown in Fig. 5a to-gether with the probabilities of the 61-year observed flood peakdischarges. Three-parameter gamma distribution curve is fittedto the observed values and shown in Fig. 5a. Fitting the three-parameter gamma distribution is the standard procedure for floodfrequency analysis (FFA) in Russia. In the range of the availableobservations, this distribution is indistinguishable from the otherdistributions typically used for FFA (e.g. Log-Pearson type IIIdistribution).

For snowmelt flood volume, we assigned the thresholdY* = 168 mm that is also close to the maximum observed one atthe Seim River. After applying the censoring procedure with theuse of formula (10), N3 = 67 floods were selected which met thecondition Y > 168 mm. Note that not all of the selected 67 floodsare included in 78 events identified by the flow criterion: thereare 14 floods of extremely large volume and moderate peak dis-charge. The exceedance probabilities of volumes of the selectedfloods are shown in Fig. 5b together with the probabilities of the61-year observed flood volumes fitted by the gamma distribution.Like in Fig. 5a, the calculated flood volumes are shown in Fig. 5b forthe exceedance probabilities not less than 0.001.

Thus, on the basis of the hydrological model coupled with theweather generator, we estimated probabilities of floods exceeding

240 260 280 300 320 340r precipitation, mm

atic mean = 207 mm

me floods under the different winter precipitation.


the maximum observed floods in the Seim River. Although the totalnumber of runs of the hydrological model has beenN1 + N2 = 10,617 but the full physically based model has been run617 times only. For the rest set of runs (10,000), the simplified ver-sion of the model is used (only processes of snowmelt, overlandand channel flow have been taken into account). By the use ofthe simplified model for the overwhelming majority of simula-tions, we estimated extreme floods of low probabilities much fas-ter then it would be done with the use of the full model. It isimportant to stress that the suggested procedure involves bothcontinuous simulation and event simulation approaches: 617 from10,000 weather scenarios were selected on the basis of continuous

80 100 120 140Pre-me

0%

3%

5%

8%

10%

13%

15%

18%

21%

23%

26%

28%

31%

33%

36%

Num

ber o

f ext

rem

e flo

ods,

%

Climatic mean = 89 m

Fig. 9. Frequencies of occurrence of the simulated extreme flo

50 60 70 80 90March-April

0%

3%

5%

8%

10%

13%

15%

18%

21%

23%

26%

28%

31%

33%

Num

ber o

f ext

rem

e flo

ods,

%

Climatic

Fig. 8. Frequencies of occurrence of the simulated extre

simulation by the simplified hydrological model whereas 617floods were simulated on the basis of event approach using the se-lected weather scenarios. In the case of the event simulation ap-proach, the initial conditions, at May 1st, were chosen as follows.Initial snow depth and, consequently, water content of snow, aswell as soil ice content were set equal to zero. Initial soil moisturecontent was set equal to field capacity and uniformly distributedwithin the soil layer. Taking into account that in the Seim River ba-sin annual maximum floods are generated during spring melt per-iod in March–April, one can believe that the simulated snowmeltfloods do not sensitive to the errors in the assigned initial condi-tions at May 1st of the previous year.

160 180 200 220 240lt SWE, mm

m

ods under the different pre-melt snow water equivalent.

100 110 120 130 140 precipitation, mm

mean = 75mm

me floods under the different spring precipitation.


4.4. Analysis of genesis of simulated extreme floods

Next we turn to the analysis of genesis of the simulated extremefloods exceeding the maximum observed flood in the Seim River.For the analysis, we selected those 78 simulated floods whichmet the condition Qmax > 2200 m3 s�1. Extreme floods can becaused by unusual combinations of meteorological factors and run-

0

5

10

15

20

25

15.11 29.11 13.12 27.12 10.01 24

Pre

cipi

tati

on, m

m/d

ay

-40-30-20-10

0102030

15.11 29.11 13.12 27.12 10.01 24

15.11 29.11 13.12 27.12 10.01 24

15.11 29.11 13.12 27.12 10.01 24.

Air

Tem

pera

ture

, OC

0

50

100

150

200

Snow

Wat

erE

quiv

alen

t, m

m

0500

10001500200025003000

20.03 27.03 03.04

Q,

3 /

0

0.103

0.206

0.309

0.412

0.515

Soil

Wat

er C

onte

nt

Total water content

0.01

0.1

1

10

100

1000

10000

15.11 29.11 13.12 27.12 10.01 24.0Satu

rate

d C

ondu

ctiv

ity,

m

m/d

ayc

M(a)

(b)

(c)

(d)

(e)

(f)

Fig. 10. Temporal changes of conditions causing generation of the extreme flood: a – dailand ice content; e – saturated hydraulic conductivity; f – extreme flood hydrograph.

off generation mechanisms which have never been registered dur-ing the period of measurements. Using the presented technique,one can reproduce great diversity of possible weather scenariosand hydrological processes forced by these scenarios. As a result,an opportunity arises to analyze conditions of flood formation,including critical conditions of floods exceeding the maximum ob-served flood.

.01 07.02 21.02 07.03 21.03 04.04 18.04

.01 07.02 21.02 07.03 21.03 04.04 18.04

.01 07.02 21.02 07.03 21.03 04.04 18.04

01 07.02 21.02 07.03 21.03 04.04 18.04

10.04 17.04 24.04

Ice content of upper 20-cm soil layer

of upper 20-cm soil layer

1 07.02 21.02 07.03 21.03 04.04 18.04

y precipitation; b – daily air temperature; c – snow water equivalent; d – total water


Analysis of the air temperatures for the winters preceding thesimulated extreme floods has shown that these floods are formed,mostly, after cold winters. Climatic mean temperature for this sea-son is �3.4 �C in the Seim River basin, while the extreme floods fol-low the winters with mean calculated temperature of �5.4 �C.Note, that the calculated extreme floods are formed both afterthe colder winters (up to �8.6 �C) and after the warmer ones(the maximum mean winter temperature is �1.5 �C). Frequenciesof occurrence of the extreme snowmelt floods under the differentmean winter temperature are shown in Fig. 6a. As one can see fromthis figure, the extreme floods exceeding the maximum observedflood in the Seim River are formed most often after the winterswith mean temperatures about �6 to �7 �C. Decreasing the airtemperatures resulted in increasing the snow accumulation periodand decreasing the number of the winter thaws. However the gov-erning factor, which influences on the extreme floods and is theconsequence of the fall of temperature, is later dates of beginningof melt in comparison with the climatic mean date. The latter dateis 24 of March whereas, according to simulation results, melt be-gins, most often, 5–11 days later before the extreme floods(Fig. 6b). As a rule, this leads to more intensive melt and faster ris-ing of water inflow to river channels.

Winter precipitation totals are slightly larger (by 22%, in aver-age) before the simulated extreme floods than the climatic meanprecipitation (207 mm). It is seen from Fig. 7, that sometimes,the simulated extreme floods are formed after very wet winters;however, such floods are not uncommon after rather dry winters(140–160 mm of precipitation).

Climatic mean precipitation total for March–April (this is theperiod of snowmelt floods in the Seim River basin) is 75 mm. Thesimulated extreme floods are formed most often during springs,when precipitation totals are about 85–90 mm; at that, as a rule,most of precipitation falls in the beginning of melt period. Frequen-cies of occurrence of extreme snowmelt floods under the differentMarch–April precipitation total are shown in Fig. 8.

Thus, analysis of the simulation results has shown that the sim-ulated extreme snowmelt floods exceeding the maximum ob-served flood in the Seim River are generated under a wide rangeof meteorological conditions. More often such floods occur after acold and wet winter–spring period, however, a relatively warmwinter with moderate precipitation can also precede extreme flood(these situations occur in 5% of simulated extreme events). Twentypercent of the simulated extreme floods are generated when themost intensive melt of snow starts as late as in April.

Pre-melt watershed conditions, along with the consideredmeteorological factors, strongly influence on flood generation pro-cesses. Snow water equivalent (SWE), soil freezing and soil mois-ture content at the Seim River basin preceding the simulatedextreme floods are analyzed below.

According to simulations, the extreme floods are formed, mostoften, under the pre-melt SWE much larger than mean SWE pre-ceding ordinary floods. The main reasons for larger SWE areincreasing snow accumulation period and absence of the winterthaws. One can see from the histogram shown in Fig. 9, that everythird of simulated extreme floods is generated under pre-melt SWEabout 140–160 mm, i.e. 57–80% larger than the climatic meanSWE. However about 5% of such floods are formed under pre-meltSWE which is close to the climatic mean SWE.

About 20% of the simulated extreme floods are formed underthe rather shallow depth of soil freezing (less than 40 cm), how-ever, most often such floods are formed on the deeper frozen soils.

With the help of the vertically distributed model of heat andmoisture transfer (Eqs. (4) and (5)), we investigated influence of li-quid water and ice distribution over a soil profile on formation ofextreme floods. Before the beginning of melt following by the ex-treme flood formation, the total water content of the upper soil

layer (up to depth of 100 cm) is close to field capacities of the SeimRiver basin soils. However, such soil saturation before melt is typ-ical for the Seim River basin as well as for many basins located inthe forest-steppe zone of the European Russia and is not a distinc-tive feature for the extreme floods. Analysis of the simulation re-sults obtained with the help of the model of heat and moisturetransfer has shown that this distinctive feature is in the following.Before ordinary floods, moisture is quite uniformly distributed overa soil profile. At the same time, high relative saturation of theupper 10–20 cm soil layer is typical for soil moisture profile pre-ceding extreme floods. The revealed accumulation of moisture inthe upper soil layer can be caused by autumn rainfalls, winter up-ward transfer of soil moisture from deep, unfrozen layers towardsthe freezing front, and infiltration of water during winter–springthaws. High relative saturation of the upper soil layer in combina-tion with negative soil temperature leads to accumulation of iceand overcooled liquid water near the soil surface before melt. Dur-ing the intensive melt, infiltrated water freezes in the process ofinteraction with soil matrix and overcooled liquid water. As a re-sult impermeable soil layers can be formed near the soil surfaceand lead to an abrupt decrease in infiltration losses. Formation ofan impermeable layer near the soil surface over the most part ofthe catchment area is the distinctive feature of soil moisture re-gime during the extreme flood formation. To illustrate this process,temporal changes of simulated hydrometeorological conditionscausing generation of the extreme flood are shown in Fig. 10a–e.Simulated hydrograph of this flood exceeding the maximum oneobserved at the Seim River is shown in Fig. 10f. As one can see fromFig. 10d, the calculated ice content of the upper 20-cm soil layergradually increased during the winter owing to decreasing of soiltemperature. Soil freezing lead to decreasing of infiltration capac-ity of soil, for example, saturated conductivity of chernozem soildecreased from almost 2000 mm per day under the unfrozen con-ditions to 16 mm per day (Fig. 10e). In the beginning of the simu-lated melt season, the first portions of infiltrated water froze in theprocess of interaction with frozen soil that lead to abrupt increas-ing in ice content and soil conductivity fell to 2–3 mm per day. Thesubsequent intensive melt of snow occurred over the almostimpermeable soil (saturated conductivity of the upper soil layerwas less than 1 mm/day).

5. Conclusion

Inclusion of information on stochastic properties of meteorolog-ical inputs in a deterministic watershed model extends a range ofhydrological problems which can be solved with the help of thewatershed model. However for long time, beginning from the pio-neer work of Eagleson (1972), such a dynamic-stochastic approachwas applied, as a rule, for the problem of flood frequency assess-ment. Furthermore, overwhelming majority of the studies dealtwith the dynamic-stochastic approach does not take into accountspecific hydrological processes controlling snowmelt flood genera-tion, e.g. snow accumulation and melt, soil freezing and thawing,infiltration into frozen soil, etc. The main motivation for this paperwas to show advanced opportunities of the model containing, asthe deterministic component, sophisticated, distributed model ofsnowmelt runoff generation which describes the hydrological pro-cesses listed above. Specific censoring procedure has been devel-oped as the effective, time-consuming computational algorithmfor assessing extreme flood frequencies. In addition to the assess-ment of the extreme floods frequencies, the model has allowedfor the description of characteristics of the genesis of the extremesnowmelt floods. Probabilities of occurrence of such floods are verysmall and, certainly, it is unlikely to detect peculiarities of theirgenesis from the available observations. It has been shown that


the extreme snowmelt floods exceeding the maximum observedflood in the Seim River can be generated under a wide diversityof hydrometeorological conditions, including combinations ofmeteorological factors and runoff generation mechanisms whichhave never been recorded during the period of observations. Atthe same time but in rare instances, quite ordinary meteorologicalfactors and watershed conditions can lead to generation of the ex-treme floods.

Acknowledgements

I would like to thank Prof. Lev Kuchment for many inspiring dis-cussions which have greatly contributed to the crystallization ofthe ideas presented in this paper. The present work was carriedout as part of a research project supported by the Presidium of Rus-sian Academy of Sciences (the Basic Research Program #16).

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http://dx.doi.org/10.1002/hyp.6787

http://dx.doi.org/10.1029/2004WR003439

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